"Banking" can also be done in order to move cards from your unit list back into your Inbox.
This is useful when your collection of cards grows and you need to make space for 'feeder' units that you intend to use to 'enhance' other cards.
To "bank" units, simply trade 5 cards to a trusted ally. They can cancel your trade, and the cards will go into your inbox. This is different than the process for banking Luna, because cancelled Luna trades go right back into your Luna Vault.
I recommend first sending a message to all your allies from the 'Allies' page to find out who is active and available to help you bank units. It is inconvenient to have cards trade-locked by an ally who then goes inactive for a few days. >_<